Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound
This is an incremental improvement for Bayesian optimization in constrained settings, addressing a specific bottleneck in existing methods.
The paper tackles constrained Bayesian optimization by proposing a novel variant of Max-value Entropy Search (CMES-IBO) that incorporates feasibility uncertainty and ensures non-negativity, demonstrating effectiveness on benchmark functions and real-world problems.
Max-value entropy search (MES) is one of the state-of-the-art approaches in Bayesian optimization (BO). In this paper, we propose a novel variant of MES for constrained problems, called Constrained MES via Information lower BOund (CMES-IBO), that is based on a Monte Carlo (MC) estimator of a lower bound of a mutual information (MI). Unlike existing studies, our MI is defined so that uncertainty with respect to feasibility can be incorporated. We derive a lower bound of the MI that guarantees non-negativity, while a constrained counterpart of conventional MES can be negative. We further provide theoretical analysis that assures the low-variability of our estimator which has never been investigated for any existing information-theoretic BO. Moreover, using the conditional MI, we extend CMES-IBO to the parallel setting while maintaining the desirable properties. We demonstrate the effectiveness of CMES-IBO by several benchmark functions and real-world problems.